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Ordering of Elliptic Flow at High Pt

Ordering of Elliptic Flow at High Pt. Zi-wei Lin The Ohio State University. Quark coalescence model v2 at high Pt: dominance of leading quark from phase space v2 from quarks to hadrons flavour ordering special cases, and the quark counting rule

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Ordering of Elliptic Flow at High Pt

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  1. Ordering of Elliptic Flow at High Pt Zi-wei Lin The Ohio State University • Quark coalescence model • v2 at high Pt: • dominance of leading quark from phase space • v2 from quarks to hadrons • flavour ordering • special cases, and the quark counting rule • What have been neglected in the analysis? • Summary Z.W.L.&Ko,PRL89 Transverse Dynamics at RHIC BNL, March 2003

  2. v2 data at low Pt v2 at a fixed pt follow mass scaling: v2(M) < v2(m) for M > m Huovinen et al, PLB503 STAR, PRL87

  3. v2 data at high Pt (@130GeV) for identified hadrons: STAR, PRL89

  4. v2 (@200GeV) for identified hadrons: Filimonov, QM02 see H. Huang, R. Snellings’s talks

  5. Framework: the Quark Coalescence Model Near hadronization, gluon may decouple (decayed or absorbed), thus we may consider only constituent quarks just before the phase transition • for Multipliticy: coalescence factor (wavefunction) quark distributions (phase space) • Momentum distributions:

  6. Dominance of the leading parton at high Ptfrom phase space Consider a formation of high Pt meson from a) a leading q and a soft qbar (~Pt+soft) b) q and qbar with equal momentum (Pt/2+Pt/2) If Pt/2 is still high, and only consider phase space: due to power-law enhancement of high Pt partons scenario a) dominates -aPt e n 1/Pt parton spectra just before phase transition

  7. Parton v2 => hadron v2 if hadronic effects on v2 are neglected, then for mesons: leading q or qbar azimuthal angle w.r.t. reaction plane Ci: coalescence probability, for a high Pt parton to capture a soft parton i and form a hadron

  8. for SU(3) hadrons at a fixed high Pt: same for all SU(3) hadrons at a given high Pt

  9. Impose isospin symmetry & s-sbar symmetry: assume, for variables : At RHIC, pi+/pi-, K+/K-~1 depends on 2 ratios:

  10. At RHIC, pbar/p~0.7 Further impose q-qbar symmetry: depends on 1 ratio: Flavour ordering at a fixed high Pt: gives • 2 independent relations (out of 3), can be checked using v2 of 4 particle species:

  11. Several limits: Some limits: 1) leading light quark 2) leading s quark 3) Quark-counting rule

  12. mass vs flavour ordering at low Ptat high Pt K curve will cross N & Lambda curves A schematic plot At high Pt:

  13. Neglected in this analysis: • Independent fragmentation of parton jets -> may start to dominate at very high Pt • wavefunction overlap of coalescencing partons: (only phase space distributions are considered here) Ci: only depends on flavour i of the soft parton, not on flavour of the high pt parton or relative momenta Discussed recently by: Fries et al, nucl-th/0301087 Greco,Ko&Levai, nucl-th/0301093 Molnar&Voloshin, nucl-th/0302014 see D. Molnar, R. Fries’s talks

  14. wavefunction overlap of coalescencing partons: 1) The limit of wide overlap (in relative momentum): -> phase space dominates -> flavour ordering 2) Wavefunction with exponential tail in radius: -> dipole-form power-law suppression -> qualitatively the same • 3) Gaussian wavefunction: -> exponential suppression of large relative momenta between coalescing quarks ->qualitatively different • 4) The limit of narrow overlap: baryon from 3 quarks of Pt/3, meson from 2 quarks of Pt/2 Molnar&Voloshin, nucl-th/0302014

  15. Summary • Phase space consideration from the quark coalescence model: v2(high Pt) may follow flavour ordering instead of mass ordering for v2(low Pt) • If , all SU(3) hadrons have same v2 at a given high Pt • If , flavour ordering follows in isospin & quark-antiquark symmetric matter • The special case of corresponds to quark counting rule • Effects of wavefunctions (for the coalescence probability) and independent fragmentation can change the picture, recently discussed by several groups

  16. v2 data at high Pt STAR, PRL90

  17. Elliptic flow (v2): azimuthal asymmetry in transverse momentum Y X: impact parameter Z: beam axis

  18. Elliptic Flow at Really High Momentum • STAR charged hadron elliptic flow out to pT = 12 GeV/c ! • finite v2 beyond pT = 6 GeV/c for semi-central • decrease of v2 in central? Peitzmann, QM02

  19. A schematic plot for

  20. Coalescence inALCOR Biro et al, PLB347; Biro, hep-ph/0005067; Zimanyi et al, Heavy Ion Phys4,15; PLB472, hep-ph/0103156 ALgebraic COalescence Rehadronization model Near hadronization, gluon may decouple (decayed or absorbed), thus consider only constituent q+qbar: coalescence factor 2Nf normalization factors, determined from 2Nf equations for quark # conservation:

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